User:Julia Hartman
Girl's Night
Audrey, Brooke and Caroline are planning a long movie night. They want to binge-watch some films together from their favorite director. But they can't decide on the selection of movies, because they have a deal that they must all agree on the films they watch. Moreover, their preferences are very different, and there are eleven titles to choose from. After long discussions, Caroline proposes the following: "Each one of us independently writes a list of five of the eleven titles. The order is not important." Audrey is enthusiastic about the idea. Brooke, on the other hand, is skeptical, saying, "I don't think we can agree on more than two titles using this procedure."
What is the probability that more than two of the same titles are found on all three lists?
Fair is not enough
A biomedical research group consists of five doctoral students: A, B, C, D, E. According to the valid doctoral regulations, a doctorate can be awarded cumulatively for publishing three papers in specialist journals. The doctoral supervisor, Professor L, says "I bet five papers would do it, we can get that many written up quickly. Of course, I'll be on all the papers as the lab supervisor. And my friends from industry, S, T, U, V, & W, can each be on one of the papers."
Due to numerous disputes regarding the fair order and distribution of authors' names and countless complaints to various ombud institutions, the following conditions must be strictly followed:
- Each doctoral student must be involved in exactly three publications and exactly once each as first, second and third author.
- No doctoral candidate may be named more than once before another doctoral candidate.
- Each pair of doctoral students cannot be mentioned more than twice.
Furthermore, the usual custom must apply:
- The doctoral supervisor is last author and
- one of the industry persons is the next-to-last author on each publication.
Questions from (good) scientific practice
- Is it possible to award doctorates to all five doctoral candidates with only five articles, taking into account the above conditions?
- How do you distribute and order the doctoral candidates among the articles as fairly and conflict-free as possible?